Noise Effects on Synchronized Globally Coupled Oscillators

The synchronized phase of globally coupled nonlinear oscillators subject to noise fluctuations is studied by means of a new analytical approach able to tackle general couplings, nonlinearities, and noise temporal correlations. Our results show that the interplay between coupling and noise modifies the effective frequency of the system in a non trivial way. Whereas for linear couplings the effect of noise is always to increase the effective frequency, for nonlinear couplings the noise influence is shown to be positive or negative depending on the problem parameters. Possible experimental verification of the results is discussed.Comment: 6 Pages, 4 EPS figures included (RevTeX and epsfig needed). Submitted to Phys. Re

Nonlinear dynamics of coupled transverse-rotational waves in granular chains

The nonlinear dynamics of coupled waves in one-dimensional granular chains with and without a substrate is theoretically studied accounting for quadratic nonlinearity. The multiple time scale method is used to derive the nonlinear dispersion relations for infinite granular chains and to obtain the wave solutions for semiinfinite systems. It is shown that the sum-frequency and difference-frequency components of the coupled transverse-rotational waves are generated due to their nonlinear interactions with the longitudinal wave. Nonlinear resonances are not present in the chain with no substrate where these frequency components have low amplitudes and exhibit beating oscillations. In the chain positioned on a substrate two types of nonlinear resonances are predicted. At resonance, the fundamental frequency wave amplitudes decrease and the generated frequency component amplitudes increase along the chain, accompanied by the oscillations due to the wave numbers asynchronism. The results confirm the possibility of a highly efficient energy transfer between the waves of different frequencies, which could find applications in the design of acoustic devices for energy transfer and energy rectification

Enzyme kinetics for a two-step enzymic reaction with comparable initial enzyme-substrate ratios

We extend the validity of the quasi-steady state assumption for a model double intermediate enzyme-substrate reaction to include the case where the ratio of initial enzyme to substrate concentration is not necessarily small. Simple analytical solutions are obtained when the reaction rates and the initial substrate concentration satisfy a certain condition. These analytical solutions compare favourably with numerical solutions of the full system of differential equations describing the reaction. Experimental methods are suggested which might permit the application of the quasi-steady state assumption to reactions where it may not have been obviously applicable before

On phenomenon of scattering on resonances associated with discretisation of systems with fast rotating phase

Numerical integration of ODEs by standard numerical methods reduces a continuous time problems to discrete time problems. Discrete time problems have intrinsic properties that are absent in continuous time problems. As a result, numerical solution of an ODE may demonstrate dynamical phenomena that are absent in the original ODE. We show that numerical integration of system with one fast rotating phase lead to a situation of such kind: numerical solution demonstrate phenomenon of scattering on resonances that is absent in the original system.Comment: 10 pages, 5 figure

The self-consistent gravitational self-force

I review the problem of motion for small bodies in General Relativity, with an emphasis on developing a self-consistent treatment of the gravitational self-force. An analysis of the various derivations extant in the literature leads me to formulate an asymptotic expansion in which the metric is expanded while a representative worldline is held fixed; I discuss the utility of this expansion for both exact point particles and asymptotically small bodies, contrasting it with a regular expansion in which both the metric and the worldline are expanded. Based on these preliminary analyses, I present a general method of deriving self-consistent equations of motion for arbitrarily structured (sufficiently compact) small bodies. My method utilizes two expansions: an inner expansion that keeps the size of the body fixed, and an outer expansion that lets the body shrink while holding its worldline fixed. By imposing the Lorenz gauge, I express the global solution to the Einstein equation in the outer expansion in terms of an integral over a worldtube of small radius surrounding the body. Appropriate boundary data on the tube are determined from a local-in-space expansion in a buffer region where both the inner and outer expansions are valid. This buffer-region expansion also results in an expression for the self-force in terms of irreducible pieces of the metric perturbation on the worldline. Based on the global solution, these pieces of the perturbation can be written in terms of a tail integral over the body's past history. This approach can be applied at any order to obtain a self-consistent approximation that is valid on long timescales, both near and far from the small body. I conclude by discussing possible extensions of my method and comparing it to alternative approaches.Comment: 44 pages, 4 figure

Coexisting periodic attractors in injection locked diode lasers

We present experimental evidence for coexisting periodic attractors in a semiconductor laser subject to external optical injection. The coexisting attractors appear after the semiconductor laser has undergone a Hopf bifurcation from the locked steady state. We consider the single mode rate equations and derive a third order differential equation for the phase of the laser field. We then analyze the bifurcation diagram of the time periodic states in terms of the frequency detuning and the injection rate and show the existence of multiple periodic attractors.Comment: LaTex, 14 pages, 6 postscript figures include

Gravitational radiation reaction and inspiral waveforms in the adiabatic limit

We describe progress evolving an important limit of binary orbits in general relativity, that of a stellar mass compact object gradually spiraling into a much larger, massive black hole. These systems are of great interest for gravitational wave observations. We have developed tools to compute for the first time the radiated fluxes of energy and angular momentum, as well as instantaneous snapshot waveforms, for generic geodesic orbits. For special classes of orbits, we compute the orbital evolution and waveforms for the complete inspiral by imposing global conservation of energy and angular momentum. For fully generic orbits, inspirals and waveforms can be obtained by augmenting our approach with a prescription for the self force in the adiabatic limit derived by Mino. The resulting waveforms should be sufficiently accurate to be used in future gravitational-wave searches.Comment: Accepted for publication in Phys. Rev. Let

Reduced dynamics and symmetric solutions for globally coupled weakly dissipative oscillators

This is a preprint of an article whose final and definitive form has been published in DYNAMICAL SYSTEMS © 2005 copyright Taylor & Francis; DYNAMICAL SYSTEMS is available online at: http://www.informaworld.com/openurl?genre=article&issn=1468-9367&volume=20&issue=3&spage=333Systems of coupled oscillators may exhibit spontaneous dynamical formation of attracting synchronized clusters with broken symmetry; this can be helpful in modelling various physical processes. Analytical computation of the stability of synchronized cluster states is usually impossible for arbitrary nonlinear oscillators. In this paper we examine a particular class of strongly nonlinear oscillators that are analytically tractable. We examine the effect of isochronicity (a turning point in the dependence of period on energy) of periodic oscillators on clustered states of globally coupled oscillator networks. We extend previous work on networks of weakly dissipative globally coupled nonlinear Hamiltonian oscillators to give conditions for the existence and stability of certain clustered periodic states under the assumption that dissipation and coupling are small and of similar order. This is verified by numerical simulations on an example system of oscillators that are weakly dissipative perturbations of a planar Hamiltonian oscillator with a quartic potential. Finally we use the reduced phase-energy model derived from the weakly dissipative case to motivate a new class of phase-energy models that can be usefully employed for understanding effects such as clustering and torus breakup in more general coupled oscillator systems. We see that the property of isochronicity usefully generalizes to such systems, and we examine some examples of their attracting dynamics

Hamiltonian formulation of nonequilibrium quantum dynamics: geometric structure of the BBGKY hierarchy

Time-resolved measurement techniques are opening a window on nonequilibrium quantum phenomena that is radically different from the traditional picture in the frequency domain. The simulation and interpretation of nonequilibrium dynamics is a conspicuous challenge for theory. This paper presents a novel approach to quantum many-body dynamics that is based on a Hamiltonian formulation of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of equations of motion for reduced density matrices. These equations have an underlying symplectic structure, and we write them in the form of the classical Hamilton equations for canonically conjugate variables. Applying canonical perturbation theory or the Krylov-Bogoliubov averaging method to the resulting equations yields a systematic approximation scheme. The possibility of using memory-dependent functional approximations to close the Hamilton equations at a particular level of the hierarchy is discussed. The geometric structure of the equations gives rise to reduced geometric phases that are observable even for noncyclic evolutions of the many-body state. The formalism is applied to a finite Hubbard chain which undergoes a quench in on-site interaction energy U. Canonical perturbation theory, carried out to second order, fully captures the nontrivial real-time dynamics of the model, including resonance phenomena and the coupling of fast and slow variables.Comment: 17 pages, revise